摘要
设D为n阶本原有向图,对于D中的每一对顶点x,y,存在正整数m,1≤m≤n,在D中总能找到m个不同的顶点v1,v2,…,vm,使得x和y到vi(1≤i≤m)都存在k长的途径,上述k中的最小者称为D的广义Competition指数(m-Competition指数).广义Competition指数是本原指数和Scrambling指数的推广.采用图论与组合矩阵论的方法,对几类本原有向图Scrambling指数极图的广义Competition指数进行研究,给出了这几类极图的广义Competition指数.
For a positive integer m, where 1≤m ≤ n, the generalized Competition index （m-Competition in- dex） of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y, there exist m distinct vertices v1, v2 ,…, vm such that there exist walks of length k from x to v1 and from y to vi for 1 ≤i≤m. The generalized Competition index is a generalization of the exponent and the Scrambling index of a primitive digraph. By using the method of graph theory and combinatorial matrix theo- ry, the generalized Competition indices of some extremal digraphs in Scrambling indices of primitive digraphs is investigated and the generalized Competition indices of these extremal digraphs is obtained.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2014年第4期365-369,共5页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金资助项目(11071227)
山西省回国留学人员科研资助项目(2012-070)
中北大学校基金资助项目
作者简介
杜建伟（1979～），男，讲师，博士生，主要从事图论与组合矩阵论的研究．
